Question

-. If cosec 0 + cot0 = 5, find sino and coso.​

Answer 1

Step-by-step explanation:

Cosecx + Cotx = 5

1/Sinx + Cosx / Sinx = 5

1+ Cosx/ Sinx = 5

1 + Cosx = 5 Sinx

Squaring both sides

Cos^2x + 2 Cosx + 1 = 25 Sin^x

Cos^2x + 2 Cosx + 1 = 25 ( 1 - Cos^2x )

Cos^2x + 2 Cosx + 1 = 25 - 25Cos^2x

26 Cos^2x + 2 Cosx - 24 = 0

2 ( 13 Cos^2x + Cosx - 12 = 0

13 Cos^2x + Cosx - 12 = 0

13 Cos^2x + 13 Cosx -12 Cosx - 12 = 0

13 Cosx ( Cosx + 1 ) -12 ( Cosx + 1 ) = 0

( 13 Cosx - 12 ) ( Cosx + 1 ) = 0

Cosx = 12/13 or Cosx = -1

Sin x = 5/13 or Sin x = 0